zankaon

March 20, 2017

Can manifolds change; or are they invariant?

Filed under: Letters from Ionia — Tags: , — zankaon @ 5:12 pm

Manifold concept can, in a simplified sense, be refered to as just a surface. Thus shape is irrelevant; hence change in shape is not pertinent.

Manifold can be rendered as continuum; that is an inbetweeness quality, wherein one has a mapping of nearby elements of respective sets. Can one even have a minimum number (3) of elements required to define closeness and inbetweeness?


So can a manifold change; that is change it’s continuum? Or add additional inclusiv.e new continua vis a product space construction, giving successively a new higher dimensional space?


Would bifurcation and merging of manifolds be impossible, even of same continua? Exemplified by no merging of hot Jupiters’ with respective star, even over billion of years? Thus also consistent with no coalescence of compact objects? Also would above be compatable with no bifurcating of manifolds, as in eternal chaotic inflation, nor with merging of 3-branes, nor of patches of different manifold arising within a given manifold, nor of non-manifold suddenly appearing i.e. singularity etc.?


Thus are manifolds stable? Thus no creation nor destruction of manifolds. Hence for example, consistent with a divergent set of entangled always disjoint manifolds?


Would all of this seem consistent with concept of manifolds being truculent, and difficult to deal with? As if  they want to be left alone; perhaps because they are not capable of change i.e. always invariant? 

Modified Set Model at HTTP://sites.Google.com/site/zankaon

March 19, 2016

How typical is our evolving 3-manifold?

Filed under: Letters from Ionia — Tags: , , , — zankaon @ 6:49 pm

If functions (defining continuity of manifolds?) don’t behave well, such as continuous but non-typical, and hence not smooth, and likewise for our overall Regional volume V_R  3-manifold, which is mainly characterized (hence mathematically more typical) by non-differentiated finer than Planck scale; then is not just our coarser than Planck scale, a very atypical perspective, mathematically speaking?

Might the nature of time , in regards to our evolving 3-manifold and alleged divergent set, System S≡{U_T’, …} of total universes, wherein U_T≡{{V^3_R}_p}, be considered as both always exponentially changing, and thus analytical; likewise for mapping to integers in such  model ?

Thus would the ‘flow of time‘  seem to be  smooth and analytical? In contrast, our finite appearing (coarser than Planck scale) 3-manifold high perch has just finite order differentiation; whereas the overall coarser to finer 3-manifold is not smooth. So our mixture of 2 manifolds would seem to differ in smoothness attribute, as well as continuity, but not in cardinality.

So we would seem to reside in a mixture of 2 topologically inequivalent manifolds, an exponentially changing 1-manifold being well behaved (smooth, and analytical?), but not typical for most manifolds. Whereas the overall coarser to finer 3-manifold is not well behaved (non-smooth), but typical for manifolds; such as 3-manifold version of Weirstrauss function?

That is, what we perceive as a whole, is actually a composite of 2 topologcally inequivalent manifolds, described both as well behaved but not typical for temporal change; while the coarser to finer scale is not well behaved yet typical, in comparison to most other manifolds.

also  zankaon website, SRM page.

May 1, 2015

Variance from idealized forms i.e. patterns, for nature, and mathematics? Intrinsic common characteristics for both world views?

We often times render the world around and within, with examples and renditions, based on simplifications or perhaps internalized ideals. Such as for example the circle, although it is only a specialized case of an ellipse, and of equiangular spiral.

However manifestations are usually imperfect, even in principle. For example, homogeneity versus possible heterogeneity of Big Bang nucleosynthesis, anisotropy 10^-5 of cosmic background radiation, and clustering for early universe vs uniform distribution of galactic/cluster mass. Hence the homogeneity and isotropy of cosmological principle would seem to be just an idealization. Thus just the pursuit of randomness, and not it’s attainment. So would it seem that our world is just the result of such imperfections, such as matter / anti-matter asymmetry?

Also one has Newton’s emphasis on uniformity, such as for flow of time, and for initial base line of uniform change in general, such as inertia concept, and as implied by usage of suggestive terms, fluent/fluxion. Also one has the idealization of Minkowski manifold, rather than always curvature and mass, with Minkowski manifold just an idealized tangent surface.

Locally one has absence of perfect order; rather always an entropic description, such as unattainably of absolute zero Kelvin. Metaphorically one might express it as if similar to no ‘Dirac like’ one value function; rather always energy being partitioned more diversely i.e. ‘energy – the handmaiden of entropy’.

Conversely, also no idealized complete disorder i.e. not just an entropic description; rather always some information descriptive, such as emphasized in Ramsey’s theorem. Again, randomness, both in physical and mathematical sense (?), would seem to be just an idealization.

Also one has Lyle’s idealized uniformitarianism of geological change, and Darwin’s continuation of such simplification and assumption of uniformity (slower implied uniform rate of change) to biological evolution.

And in mathematics, one has clustering of primes, rather than a uniform distribution. Likewise for the rationals, since the primes are a specific case of rationals. Hence the distribution of Cantor dust would seem to be clustered  i.e. not uniform.

Perhaps other mathematical examples, such as π?
J. Wallis: π/2 = 2/1 x 2/3 x 4/3 x 4/5 x 6/5 x 6/7 …

Thus an irrational number can be constructed from infinite multiplicative series of rationals i.e. integer ratios. Thus can one have it both ways with π; that is both an irrational and also a rational rendering?

However although assuming it is a divergent series of rational terms, still the summation would seem statistically to reside in the greater ‘sea’ i.e. greater cardinality, of irrationals. This could be visualized by the complement of the clustered Cantor dust of discarded rationals; that is a greater ‘sea’ of irrationals.

Also does irrational rendition of π’s involvement with special case of the circle seem so unusual, especially since the circle is just a special case of an ellipse, and of equiangular spiral, wherein for both, π is not descriptive?

Would this all suggest local imperfections i.e. non-idealization, being more suitable for our rendering, modeling, and even in a platonic sense, more typical for nature and even for mathematics? For example, would our world seem just an imperfect rendition i.e. for example, the result of such matter / anti-matter asymmetry? Is then the modified global scale of Spiral Rotation Model (with no parameters, nor degrees of freedom) a counter example, and complement, to such manifested imperfections?
see zankaon site

IMG_20150518_102955

Is this discussion then relevant to Plato’s emphasis on inapparent idealized forms behind imperfect manifestations? However herein variation from such idealization, such as differing from forms, is emphasized. In overall sense, then are there similarities between not only philosophical and physical models, but also inclusive of ethical models? see zankaon site.

Also if rationals are clustered, and matchable to coarser to finer scale, then would such pattern also be consistent with manifested imperfections, such as early universe clustering, possible BB heterogeneous nucleosynthesis, CMB anisotropy, lack of randomness or perfect local order (such as zero Kelvin); also would such clustering of rationals be consistent with mathematical imperfections, such as lack of randomness description i.e. conjecture?

So is imperfection part of the scheme of things, both physical and even for mathematics?

Might there be other examples in nature, or in physical modeling, or even for mathematics per se, that also might be considered as overall intrinsic common characteristics?

Are manifolds difficult to deal with in mathematics, and also in physical models? That is, even though one can run up and down a binary tree i.e. merging and bifurcating, with manifolds as elements, still are such mathematical objects recalcitrant to manipulation?

For example, such as for merging 3-brane manifolds? Also budding (bifurcating) manifolds, such as for eternal chaotic inflation, would seem problematic, mathematically. Also creation of manifold i.e. continuity, from null set would seem problematic, even if not so for a number set?

Also creation, and destruction, of manifolds, such as for ‘beginning’, or any ending, of 3-manifold ‘universe’, would seem difficult. Also disruption of 3-manifold, such as so-called tear (Big Rip model) or singularity construct, would seem problematic in regards to such continuity disturbance. Also alleged resistance to deformation of our 3-manifold i.e. so-called law of inertia of manifold, could be considered as if manifolds want to be left unperturbed.

So are manifolds another example, whether in nature, or for physical models, or even for mathematical world per se, of a common intrinsic characteristic, residing in intersection of such 2 world views (physical and mathematical), such as represented in a Venn diagram below? Likewise for alleged clustered rational number set and thus for primes, as discussed above?

Intersection of 2 world views – mathematical and physical​

Therefore do such two examples denote built-in general common characteristics; thus serving as consistency arguments, and explanatory of general manifestations, such as imperfection and truculent manifolds i.e. incapable of change?   TMM

 zankaon website for further elaboration.

May 18, 2014

Plato’s musings: a larger more general pattern (i.e. form) descriptive of nature?

Filed under: Letters from Ionia — Tags: , , , , , , , — zankaon @ 1:14 pm

In step with Plato’s musings in regards to Forms i.e. patterns, might there be a most general pattern in a description of nature? Entropy, in it’s various renditions, and as the Second Law of thermodynamics, is very general, and survived the quantum and relativistic revolutions. Might one generalize further from such entropy construct; thus perhaps resulting in a broader applicability?

MSM (Modified Set Model) Generality:   an ongoing maximizing (or tendency toward maximizing) of the cardinality of sets (in comparison to alternative scenarios), for all stages and for all scales of manifold(s). 

Even though entropy and information is just locally generated in the model, still the construct entropy summation for over a positive definite MGS instant, has been utilized sparingly as a modified global interdependent variable. However the alleged divergent non-smooth finer than Planck scale, and alleged divergent analytical temporal sequence, such as for System S{UT, …}, and thus set of MGSs (Modified Global Simultaneity) i.e. common cosmic time, could be considered as consistent with such Generality. Thus such Generality would seem to apply to both M3m and M1m manifolds i.e for all scales and for all stages of endless evolving System S{UT, …}.

MSM Generality is considered as an abstraction and generalization from entropy concept. That is, for greater cardinality of a set, then more re-arrangements, and hence increased contribution to alleged always monotonically increasing entropy generation. Likewise allegedly a concomitant ongoing maximizing of information generation in comparison to alternative scenarios; even though entropy can be defined as a loss of information, and information can be described as a loss of entropy. ∆s1≡-∆Iand ∆IΞ-∆s2 respectively, with allegedly always ∆s1>∆I2 .

A practical example of such ongoing maximizing of entropy and information, would be us, and our ingestion of food (energy); most of which is broken down into smaller more numerous parts, and radiated as infrared radiation, in order for us to maintain a constant core etc. body temperature i.e. homothermic. Approximately 5% is utilized as free energy i.e. work, for structure and function (physiology); that is information generation.

What might be further predictions of such a model? The fermion mass spectrum would seem consistent with such MSM Generality. Also the modified black hole with polar jets, would seem consistent, and a prediction of, such model. That is, both scenarios would seem consistent with a further increasing entropy in comparison to alternative scenarios. For example, the increased surface area of such modified BH, with respective polar vertices, would be consistent with an increased entropy generation. Also the constraint of polar jets would seem to enhance information generation.

In addition, the presence of longitudinal polarization and thus mass in the universe, allows for more interactions, and hence is consistent with more entropy generation. Thus obviating the query as to the origin of mass. That is, MSM Generality would seem consistent with always the presence of mass, such as fermion mass spectrum, even at the extreme of rm minimum stage of 3-manifold evolution.

Also MSM Generality would seem consistent with the System rendered as an evolving set of manifolds; and not consistent with the complement (i.e. null set) of such System, in domain of discourse. Thus MSM Generality would not seem consistent with a special condition scenario for the System (i.e. quanta and manifold) or number set, being generated from null set. In fact the null set would represent the minimizing of cardinality of a set; the antithesis i.e. opposite, of MSM Generality.

In context of the model, one might further compare the System and it’s complement, null set. What do they have in common; they both are sets. What do they not have in common? The System set(s) has elements; whereas the complement does not. For the System, one allegedly has MSM Generality: an ongoing maximizing of cardinality of elements of sets; whereas the complement has a minimizing of elements of a set. Also the System has a manifold (i.e. topology) description, in the form of a mixed continuity, consisting of M3m and M1m manifolds; whereas the complement does not have a continuity description. So other than set construct, the System and it’s complement, not-System, would seem to define each other, in the domain of discourse.  TMM

also see https://sites.google.com/site/zankaon

the opposite of a great truth is also a great truth.

                                                 T. Mann                                                      

March 3, 2014

Are all 3-manifolds smoothable?

Filed under: Letters from Ionia — Tags: , , , — zankaon @ 7:28 pm

Mathematically supposedly all 3-manifolds are smoothable. However in physical models, for near to Planck scale, the manifold is no longer differentiable. In some speculative physical models, one allegedly still has a continuum i.e. manifold, for finer than Planck scale, with matching to rational set. Does such model serve as a counter example to the mathematical statement that all 3-manifolds are smoothable?

See https://sites.google.com/site/zankaon  for more details

January 9, 2012

Gravity waves from within black hole? Invariance of manifolds? Polar vortex – topologically correct? Gamma ray bursts

Filed under: Letters from Ionia — Tags: , , , , — zankaon @ 6:23 pm

Whether considering Newtonian space, relativity spacetime model, Hubble expansion, or SRM speculative model, one is referring to a manifold concept, which has no propagator construct in contrast to quantum world. Hence a radical and fundamental difference between 2 perspectives of nature. Extreme curvature of black hole results in event horizon, which describes inability of quanta to escape an extreme gravitational field. Whereas any interior gravity wave formation, from extreme asymmetrical mass re-distribution (at less than horizon), such as for coalescing BHs, would not seem to be impeded from escape through BH event horizon. That is, deformation of manifold would not ‘see’ event horizon construct. Would this all seem consistent with manifold, and it’s topology, being the same for interior and exterior of black hole? Also would this seem consistent with a mathematical understanding of manifolds; such as the difficulty (impossibility?) of initiating any intersection, bifurcation (as for binary tree, with finite or infinitesimal finer scale?), or any other topological change to manifold(s); that is, invariance of mathematical objects, called manifolds? Thus can topology be utilized to set constraints on physical models; for example for Planck scale models, or for prior to Big Bang’s alleged invariant 3-manifold, together with longitudinal polarization and mass, and thus curvature? Thus for persistence of smooth manifold, together with Kepler’s 2nd Law (i.e. embodying herein modified central force), wouldn’t cyclicity seem plausible? Another example: must polar vortex form when modified black hole forms; otherwise there would be topological change – from finite, unbounded, and thus closed for no polar vortex, – to finite, bounded, and not closed, for polar vortex?

Might any simultaneous modified BH and polar vortex formation give rise to immediate (or delayed?) beam formation; thus associated sometimes with GRB? Might radiation of GRB (just narrow beam component a broader beam?) be a sampler of conditions similar to BB nucleosynthesis (10degrees K), or higher? For example, might any possible GRB in Large Magellanic Cloud have been from an existing BH, but with sudden infall (external or internal) of large mass, with perturbation of internal environment and of alleged circulation (with resultant mass re-distribution) resulting in loading of vortical beam(s); thus enhanced BB nucleosynthesis and resultant directed beams with egress of new matter and radiation, which we perceive as GRB, without a supernova? For example, there are reports of low redshift GRBs without SN for GRB 060505 at z=.089, and for GRB 060614 at z=0.125. (ref 2,3,4,5,6) Might large database for GRBs, but without associated SN, even adjusted for redshift space, suggest no relationship between the two? So is just the typical SN process not suitable for GRB beam formation? Are all GRB only from any BH source? Is LMC suggestive of earlier more active stage for our bulge, with copious SN and GRB occurrence; with the latter set larger, due to more frequent mass infall and jetting? Are narrow beam component GRBs associated only with short duration GRBs, and not with SN? Or does it matter not where a BH resides? Perhaps further enlargement of SN dastabase and associated GRB, inclusive of comparatively nearby Virgo cluster and nearby superclusters, and other low redshift space etc.?

LMC has 1010 stars; and copious BHs? Hence for a wider survey of nearby superclusters, would the incidence of SN and GRB be at least similar (directionality not withstanding), due to assumed frequent mass polar vortex infall for modified BH? Yet this would not seem so for databases, normalized to similar redshift space, for GRB and SN, is it? Might any negative findings for GRBs in LMC suggest a galactic nucleus origin for some GRB? However off galactic center GRBs have been detected. In ultraviolet, for low redshift, would a galaxy be more visible, revealing better off center GRB sites? Do any of respective elements of GRB and blazar databases coincide? Redshift and resolution are always mitigating factors. Should one assume that most GRBs are of just supernova origin (as reported, association of some long duration soft GRBs with SN)? However GRBs have been reported in elliptical galaxies, consisting mostly older stars. So is black hole (new or old) the only common theme for GRBs, irrespective of site?

Might a GRB sometimes just result from a blazar burp i.e. transient egress of increase in radiation and matter? If GRBs were just a subset of blazars, then for blazars’ set normalized to GRB redshift space, wouldn’t one expect that such dataset of blazars to be as great, or greater than, that for GRBs?  see zankaon web site TMM

2. Johan P.U. Fynbo etal Nature 444 1047-9, 21 Dec. 2006.

3. N. Gehrels, J. P. Norris, S. D. Barthelmy, J. Granot, Y. Kaneko etal Nature 444, 1044-1046, 21 Dec. 2006.

4. M. Della Valle, G. Chincarini, N. Panagia, G. Tagliaferri, D. Malesani, etal. Nature 444, 1050-1052, 21 Dec. 2006.

5. A. Gal-Yam, D. B. Fox, P. A. Price, E. O. Ofek, M. R. Davis etal Nature 444, 1053-55, 21 Dec. 2006.

6. Bing Zhang, Nature 444, 1010-1011 21 Dec. 2006.

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